Well, why does he not kill Batman in the first place? Because of his daughter. She begs him not to, and, if he did anyway, it would not be just the death/killing she does not want that she would see, but revealing himself to her as a cold-blooded murderer, which she would carry with her for the rest of her days, that makes him hold off.
Later on, in the movie, Deadshot is done with the mission - doesn't care if they get killed, doesn't care if the world ends, it was all a cynical sham and manipulation anyway. What changes his mind? Finding out his daughter was writing him letters, and that she still cared about him -
You had these the whole time? You had letters from my daughter the whole time? I'm gonna get you there. And you're gonna end this. I'm gonna carry your ass if I have to. 'Cause this shit is gonna be like a chapter in the Bible. Everybody's gonna know what we did. And my daughter is gonna know that her daddy is not a piece of shit.
So, when the Enchantress read their minds and projected their wishes, sure, Batman separated him from his daughter and took away his freedom, so there's resentment there, plus, you know, he is a killer. I didn't see anything in his fantasy where his daughter was there, watching him get his revenge, so, really, there's no contradiction between what went down when he did have the chance, and his fantasy of revenge. If the enchantress sent a fantasy of him having a happy reunion with his daughter, instead, that might just harden his resolve to stop the Enchantress. Note, also, that he does quickly snap out of it when Diablo tells them it's not real.